Riješi 316*9*10^9left(16*10^-19right)^2/664*10^-27{left(5*{10^7right)}^-2}

$$\frac{ 316 \cdot 9 \times { 10 }^{ 9 } { \left(16 \times { 10 }^{ -19 } \right) }^{ 2 } }{ 664 \times { 10 }^{ -27 } { \left(5 \times { 10 }^{ 7 } \right) }^{ -2 } }$$

Procijeni

$$\frac{2275200000000000000}{83}\approx 2,741204819 \cdot 10^{16}$$

Koraci za rješenje

Otkaži 4 u brojiocu i imeniocu.

$$\frac{9\times 79\times 10^{9}\times \left(16\times 10^{-19}\right)^{2}}{166\times 10^{-27}\times \left(5\times 10^{7}\right)^{-2}}$$

Da biste podijelili stepene iste osnove, oduzmite eksponent imenioca od eksponenta brojioca.

$$\frac{9\times 79\times 10^{36}\times \left(16\times 10^{-19}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Pomnožite 9 i 79 da biste dobili 711.

$$\frac{711\times 10^{36}\times \left(16\times 10^{-19}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Izračunajte 10 stepen od 36 i dobijte 1000000000000000000000000000000000000.

$$\frac{711\times 1000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Pomnožite 711 i 1000000000000000000000000000000000000 da biste dobili 711000000000000000000000000000000000000.

$$\frac{711000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Izračunajte 10 stepen od -19 i dobijte \frac{1}{10000000000000000000}.

$$\frac{711000000000000000000000000000000000000\times \left(16\times \frac{1}{10000000000000000000}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Pomnožite 16 i \frac{1}{10000000000000000000} da biste dobili \frac{1}{625000000000000000}.

$$\frac{711000000000000000000000000000000000000\times \left(\frac{1}{625000000000000000}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Izračunajte \frac{1}{625000000000000000} stepen od 2 i dobijte \frac{1}{390625000000000000000000000000000000}.

$$\frac{711000000000000000000000000000000000000\times \frac{1}{390625000000000000000000000000000000}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Pomnožite 711000000000000000000000000000000000000 i \frac{1}{390625000000000000000000000000000000} da biste dobili \frac{45504}{25}.

$$\frac{\frac{45504}{25}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Izračunajte 10 stepen od 7 i dobijte 10000000.

$$\frac{\frac{45504}{25}}{166\times \left(5\times 10000000\right)^{-2}}$$

Pomnožite 5 i 10000000 da biste dobili 50000000.

$$\frac{\frac{45504}{25}}{166\times 50000000^{-2}}$$

Izračunajte 50000000 stepen od -2 i dobijte \frac{1}{2500000000000000}.

$$\frac{\frac{45504}{25}}{166\times \frac{1}{2500000000000000}}$$

Pomnožite 166 i \frac{1}{2500000000000000} da biste dobili \frac{83}{1250000000000000}.

$$\frac{\frac{45504}{25}}{\frac{83}{1250000000000000}}$$

Podijelite \frac{45504}{25} sa \frac{83}{1250000000000000} tako što ćete pomnožiti \frac{45504}{25} recipročnom vrijednošću od \frac{83}{1250000000000000}.

$$\frac{45504}{25}\times \frac{1250000000000000}{83}$$

Pomnožite \frac{45504}{25} i \frac{1250000000000000}{83} da biste dobili \frac{2275200000000000000}{83}.

$$\frac{2275200000000000000}{83}$$

Faktor

$$\frac{2 ^ {19} \cdot 3 ^ {2} \cdot 5 ^ {14} \cdot 79}{83} = 27412048192771084\frac{28}{83} = 27412048192771084$$